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Beliebt Rechnen >

(\partial)/(\partial y)(x-sqrt(y^2+z^2))

Lösung

\frac{\partial}{\partial y} (x - y^{2} + z^{2})

Lösung

- \frac{y}{y ^{2} + z ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial y} (x - y^{2} + z^{2})

Behandle

x, z

als Konstanten

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial y} (x) - \frac{\partial}{\partial y} (y^{2} + z^{2})

\frac{\partial}{\partial y} (x) = 0

\frac{\partial}{\partial y} (y^{2} + z^{2}) = \frac{y}{y ^{2} + z ^{2}}

= 0 - \frac{y}{y ^{2} + z ^{2}}

Vereinfache

= - \frac{y}{y ^{2} + z ^{2}}

Beliebte Beispiele

derivative 6e^{2t}

d er i v a t i v e 6 e^{2 t}

fläche y=3x^3,y=75x

a re a y = 3 x^{3}, y = 75 x

derivative sqrt(x-3)

d er i v a t i v e x - 3

derivative 7pir^2

d er i v a t i v e 7 π r^{2}

(y^')/(sqrt(y))=6x^2

\frac{y ^{^{'}}}{y} = 6 x^{2}